Question

Find the minimum value of \(\left(p_{1}+p_{2}+p_{3}+p_{4}\right)\) where \(p_{i}\) represents position of substituents and tunctional grup in IUPAC name: \(p_{1}-\) Bromo- \(p_{2}\)-Chloro-pent- \(p_{3}\)-en- \(p_{4}\)-one \(\left(p_{1}, p_{2}, p_{1}\right.\) and \(p_{4}\) may or may not be same

Short answer

The minimum value of the sum of the positions of the substituents and functional groups in the given IUPAC name is 11, which is obtained by assigning the following positions: \(p_1 = 1\) (Bromo), \(p_2 = 2\) (Chloro), \(p_3 = 3\) (alkene double bond), and \(p_4 = 5\) (ketone carbonyl group).

Step-by-step solution

The substituent groups (bromo and chloro) need to be named in alphabetical order and assigned the lowest possible locant number (position). In this case, bromo comes first, and we have to assign a position to the bromo group. #Step 2: Naming rules for functional groups#

The functional groups (ene and one, representing alkene and ketone) have specific rules for their numbering. For an alkene, the double bond should have the lowest possible locant number, and for a ketone, the carbonyl carbon should have the lowest possible locant number (except when the carbonyl group is at position 1, the oxygen does not affect the numbering of the molecule). #Step 3: Determine positions of substituents and functional groups#

To minimize the sum of \(p_1, p_2, p_3, p_4\), we should assign the lowest possible values to each. - Assign position 1 to bromo (alphabetically first): \(p_1 = 1\) - Assign position 2 to chloro (alphabetically second): \(p_2 = 2\) - Assign position 3 to the double bond of the alkene (lowest possible locant): \(p_3 = 3\) - Assign position 5 to the carbonyl group of the ketone as it cannot be placed at position 4 following lowest locant rule knowing that position 4 is already taken by the double bond: \(p_4 = 5\) #Step 4: Calculate the minimum sum#

Now, we add the values of the positions to get the minimum value: Minimum sum = \(\left(p_{1}+p_{2}+p_{3}+p_{4}\right)\) = \(1 + 2 + 3 + 5 = 11\) So, the minimum value of the sum of the positions of the substituents and functional groups in this IUPAC name is 11.

Key concepts

Substituents

In IUPAC nomenclature, substituents are groups of atoms attached to the main carbon chain of an organic molecule. These substituents modify the properties of the molecule and must be named and positioned correctly. Key to understanding how substituents are positioned is the rule of alphabetical order. This means that when you are naming a molecule, substituents must be listed alphabetically regardless of their position on the chain.

For example, in the name "Bromo-2-Chloropentane", even if the bromo group appears after chloro on the carbon chain, it is named first because 'b' comes before 'c'. The challenge lies in assigning the correct locant number, which involves numbering the carbon chain in such a way that substituents get the lowest possible numbers, especially when added together. This minimizes confusion and makes it easier to identify specific structures, especially for molecules with multiple substituents.

Functional Groups

Functional groups play a critical role in defining the chemical properties and reactions of organic compounds. In the context of IUPAC nomenclature, common functional groups like alkenes and ketones have specific rules for their locant numbers.

Alkenes are characterized by the presence of a carbon-carbon double bond. The rule for numbering is to give the lowest possible locant number to the double bond, thereby influencing the rest of the numbering of the molecule.

Ketones have a carbonyl group, marked by a carbon atom double-bonded to an oxygen atom (C=O). In IUPAC naming, while the preference is to give the lowest possible locant number to this group, it is often placed at the end of the numbering process if another functional group, such as an alkene, must take precedence due to lower possible locant assignment.

Locant Number Rules

Locant number rules ensure that every functional group and substituent on a compound's carbon chain is assigned the smallest possible number, which helps in reducing ambiguity in naming. The lowest set of numbers is preferred, and when conflicts between different groups arise, the rules prioritize certain features over others.

In practice, alkene locants are usually prioritized due to their prominent role in determining the molecule's reactivity and structure. For example, if a ketone and an alkene are present, the alkene is normally assigned the smallest possible locant, unless the specific structure dictates otherwise.

• Begin numbering from the end of the chain nearest to a substituent or functional group that has precedence.
• Assign locants to create the smallest series possible, starting with substituents in alphabetical order, followed by functional groups.

This systematic approach allows for clarity and uniformity in the naming process, making it easier for chemists and students alike to accurately understand and communicate the structure of complex organic compounds.